ACT Math – Intermediate Algebra Quiz

Students: Take our Intermediate Algebra Quiz to identify your weaknesses in slightly advanced algebra.

Intermediate Algebra problems are the most difficult on the test. However, since they represent 15 to 20% of the ACT Math score it is a good idea to try to get at least a few points. You learned these concepts in the second part of Algebra I and in Algebra II classes.

How does it work? The Intermediate Algebra quiz consists of 20 questions. Answer as many as you feel comfortable doing so and click on Correct my quiz. You will get a page (that you can print) that will show, for each incorrect answer, your answer, the actual answer and the section to review. There is a lot of websites out there explaining math concepts, and the post “ACT Math – Intermediate Algebra Review” will direct you to online resources for each of the section you should review. You can retake the quiz when you are ready to work on the questions you skipped.

To take another CollegeGuide4Parents’ quiz, check the complete list at the bottom of this post.

Note: Want to the review before finishing the quiz? Go to post ACT Math – Intermediate Algebra Review.

Intermediate Algebra Quiz

$Question\ 1.\ Factor\ x^2-4=0$

$(x+2)^2$
$(x-2)^2$
$(x-1)(x+4)$
$(x-1)(x-4)$
$(x-2)(x+2)$

$Question\ 2.\ Factor\ x^2+8x+16=0$

$(x+2)(x+8)$
$(x-4)^2$
$(x+4)^2$
$(x-4)(x+4)$
$(x+1)(x+16)$

$Question\ 3.\ Factor\ x^2-8x+16=0$

$(x-1)(x-16)$
$(x-2)(x-8)$
$(x-4)^2$
$(x-4)(x+4)$
$(x+4)^2$

$Question\ 4.\ Solve\ x^2-8x+16=0$

$x=1\ or\ x=16$
$x=2\ or\ x=8$
$x=4$
$x=-4\ or\ x=4$
$x=-4$

$Question\ 5.\ Solve\ x^2-6=x$

$x=-1\ or\ x=6$
$x=2\ or\ x=3$
$x=-2\ or\ x=-3$
$x=2\ or\ x=-3$
$x=3\ or\ x=-2$

$Question\ 6.\ Solve\ x^2+5x-36=0$

$x=-4\ or\ x=-9$
$x=-4\ or\ x=9$
$x=4\ or\ x=9$
$x=4\ or\ x=-9$
$x=9\ or\ x=1$

$Question\ 7.\ Solve\ this\ system\ of\ equations$

$3y+2x=4\\ y+5x=10$

$x=\frac{1}{2}\ and\ y=1$
$x=2\ and\ y=0$
$x=0\ and\ y=2$
$x=-4\ and\ y=8$
$x=\frac{6}{5}\ and\ y=4$

$Question\ 8.\ Solve\ this\ system\ of\ equations$

$y=2x-2\\ 2x+y=-2$

$x=0\ and\ y=-2$
$x=-2\ and\ y=0$
$x=2\ and\ y=-2$
$no\ solution$
$infinite\ solution$

$Question\ 9.\ Solve\ this\ system\ of\ equations$

$3x+2y=6\\ y=\frac{-3x}{2}+3$

$x=1\ and\ y=\frac{3}{2}$
$x=\frac{3}{2}\ and\ y=1$
$x=2\ and\ y=0$
$no\ solution$
$infinite\ solution$

$Question\ 10.\ Solve\ this\ system\ of\ equations$

$3x+2y=6\\ y=\frac{-3x}{2}+6$

$x=1\ and\ y=\frac{3}{2}$
$x=\frac{3}{2}\ and\ y=1$
$x=-2\ and\ y=6$
$no\ solution$
$infinite\ solution$

$Question\ 11.\ If\ f(x)=-10x-3,\\ what\ is\ the\ value\ of\ f(3)\ ?$

$-27$
$27$
$-3$
$-33$
$33$

$Question\ 12.\ If\ g(x)=x^2+3x-2,\\ what\ is\ the\ value\ of\ g(-3)\ ?$

$-2$
$16$
$1$
$13$
$-3$

$Question\ 13.\ If\ f(x)=2x+3\ and\ g(x)=3x+10,\\ what\ is\ f(g(2))\ ?$

$5x+23$
$7$
$16$
$31$
$35$

$Question\ 14.\ If\ f(x)=3x+5\ and\ g(x)=\sqrt{x},\\ what\ is\ g(f(x))\ ?$

$3x+5$
$\sqrt{x}$
$3\sqrt{x}+5$
$3\sqrt{x} + 5\sqrt{x}$
$\sqrt{3x+5}$

$Question\ 15.\ Add\ these\ two\ matrices$

$\begin{pmatrix} 2&1\\ 3&5 \end{pmatrix} + \begin{pmatrix} 6&-7 \\ -8&9 \end{pmatrix}\ =$

$\begin{pmatrix} 8&8\\ 11&14\end{pmatrix}$

$\begin{pmatrix} 8&-6\\ -5&14\end{pmatrix}$

$\begin{pmatrix} -4&8\\ 11&-4\end{pmatrix}$

$\begin{pmatrix} 8&8\\ 8&8\end{pmatrix}$

$\begin{pmatrix} 12&-7\\ -24&45\end{pmatrix}$

$Question\ 16.\ Subtract\ these\ two\ matrices$

$\begin{pmatrix} 5&4\\ 3&2 \end{pmatrix} - \begin{pmatrix} 1&5 \\ 2&-5 \end{pmatrix}\ =$

$\begin{pmatrix} 6&9\\ 5&-3\end{pmatrix}$

$\begin{pmatrix} 6&9\\ 5&7\end{pmatrix}$

$\begin{pmatrix} 4&-1\\ 1&7\end{pmatrix}$

$\begin{pmatrix} 4&-1\\ 1&-3\end{pmatrix}$

$\begin{pmatrix} 5&20\\ 6&-10\end{pmatrix}$

$Question\ 17.\ Evaluate\ \log_3(81)$

$3$
$9$
$81$
$4$
$2$

$Question\ 18.\ If\ \log_x(64)=2,\ what\ is\ the\ value\ of\ x\ ?$

$4$
$8$
$64$
$32$
$2$

$Question\ 19.\ If\ \log_5(x)=2,\ what\ is\ the\ value\ of\ \sqrt{x}\ ?$

$5$
$2$
$25$
$50$
$10$

$Question\ 20.\ Solve\ 4x+3 = 8x -21$

$12$
$-12$
$-6$
$6$
$7$

How does it work? The Intermediate Algebra quiz consists of 20 questions. Answer as many as you feel comfortable doing so and click on Correct my quiz. You will get a page (that you can print) that will show, for each incorrect answer, your answer, the actual answer and the section to review. There is a lot of websites out there explaining math concepts, and the post “ACT Math – Intermediate Algebra Review” will direct you to online resources for each of the section you should review. You can retake the quiz when you are ready to work on the questions you skipped.

The CollegeGuide4Parents Math Tools

The ACT Math test focuses on concepts of pre-algebra, elementary algebra, intermediate algebra, coordinate geometry, plane geometry and trigonometry. CollegeGuide4Parents created 7 short interactive quizzes (see below for a complete list) designed to help students quickly identify the skills they need to review in each of these areas. When they are done answering a quiz, students are presented with a customized report which shows the mistakes made, the correct answers and the topics they need to work on.

Students are also directed to a review page (see below for a list of all the review pages) which shows a compilation of online resources they can consult to quickly study the concepts they have difficulties with. Review pages also include links to practice worksheets for those needing to spend extra time on some topics. Finally, the review pages also provide links to ACT problems which the students can work on once they are ready to practice.

Quizzes:

(order of operations; even and odd numbers; adding and subtracting signed numbers; multiplying and dividing signed numbers)

(factors and multiples; primes; divisibility; remainders; percentages; fractions; decimals; ratios; proportions; mean, median, and mode; probability; absolute values; exponents; square roots; series)

(substitution; polynomial simplification; linear equations; FOIL; inequalities)

(solving quadratic equations; systems of equations; functions; matrices; logarithms; and equations with variable on both sides)

(inequalities and graphs; distance between points; midpoint; coordinate plane; slope between 2 points; slope of perpendicular and parallel lines; slope-intercept form; intercept; graphs; vertex of parabola)

(lines and angles; acute, obtuse, complementary, and supplementary angles; vertical angles and parallel lines; special triangles; similar triangles; pythagorean theorem; perimeter and area of circles, triangles, and rectangles; volume of 3-dimensional shapes)

(fundamentals of trigonometry; Sine, Cosine, and Tangent; Sine, Cosine, Tangent and the right triangle; graphs of Sine, Cosine and Tangent functions; some more advanced concepts such amplitude, period, phase shift and frequency)

Review Pages:

(order of operations; even and odd numbers; adding and subtracting signed numbers; multiplying and dividing signed numbers)

(factors and multiples; primes; divisibility; remainders; percentages; fractions; decimals; ratios; proportions; mean, median, and mode; probability; absolute values; exponents; square roots; series)

(substitution; polynomial simplification; linear equations; FOIL; inequalities)

(solving quadratic equations; systems of equations; functions; matrices; logarithms; and equations with variable on both sides)

(inequalities and graphs; distance between points; midpoint; coordinate plane; slope between 2 points; slope of perpendicular and parallel lines; slope-intercept form; intercept; graphs; vertex of parabola)

(lines and angles; acute, obtuse, complementary, and supplementary angles; vertical angles and parallel lines; special triangles; similar triangles; pythagorean theorem; perimeter and area of circles, triangles, and rectangles; volume of 3-dimensional shapes)

(fundamentals of trigonometry; Sine, Cosine, and Tangent; Sine, Cosine, Tangent and the right triangle; graphs of Sine, Cosine and Tangent functions; some more advanced concepts such amplitude, period, phase shift and frequency)